Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}6x-7y &= -9 \\ -9x+4y &= -6\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $4y = 9x-6$ Divide both sides by $4$ to isolate $y$ $y = {\dfrac{9}{4}x - \dfrac{3}{2}}$ Substitute this expression for $y$ in the first equation. $6x-7({\dfrac{9}{4}x - \dfrac{3}{2}}) = -9$ $6x - \dfrac{63}{4}x + \dfrac{21}{2} = -9$ Simplify by combining terms, then solve for $x$ $-\dfrac{39}{4}x + \dfrac{21}{2} = -9$ $-\dfrac{39}{4}x = -\dfrac{39}{2}$ $x = 2$ Substitute $2$ for $x$ back into the top equation. $6( 2)-7y = -9$ $12-7y = -9$ $-7y = -21$ $y = 3$ The solution is $\enspace x = 2, \enspace y = 3$.